Comptes Rendus
Incremental energy minimization in dissipative solids
Comptes Rendus. Mécanique, Volume 331 (2003) no. 7, pp. 469-474.

The incremental energy minimization is examined as a method of determining solution paths for time-independent dissipative solids. Isothermal quasi-static deformations are considered, and the deformation work is locally decomposed into the increments in free energy and intrinsic dissipation. General conditions necessary for the applicability of the minimization procedure are derived and discussed.

Nous étudions la minimisation d'énergie excédentaire comme méthode possible de détermination des solutions sous forme de chemin de déformation pour des solides dissipatifs indépendant de temps. On considère les déformations quasi-statiques, et le travail de déformation est décomposé localement en deux parties, l'excédent d'énergie libre, et la dissipation intrinsèque. Nous discutons les conditions dérivées ici, nécessaires afin de rendre la procédure de minimisation applicable au problème posé.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-0721(03)00109-8
Keywords: Solids and structures, Dissipative materials, Plasticity, Energy, Path stability
Mot clés : Solides et structures, Matériaux dissipatifs, Plasticité, Énergie, Stabilité des chemins

Henryk Petryk 1

1 Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, 00-049 Warsaw, Poland
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Henryk Petryk. Incremental energy minimization in dissipative solids. Comptes Rendus. Mécanique, Volume 331 (2003) no. 7, pp. 469-474. doi : 10.1016/S1631-0721(03)00109-8. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00109-8/

[1] H. Petryk A consistent energy approach to defining stability of plastic deformation processes (F.H. Schroeder, ed.), Stability in the Mechanics of Continua, Proc. IUTAM Symp., Nümbrecht, 1981, Springer, Berlin, 1982, pp. 262-272

[2] H. Petryk On energy criteria of plastic instability, Plastic Instability, Proc. Considère Memorial, École Nat. Ponts Chauss., Paris, 1985, pp. 215-226

[3] H. Petryk The energy criteria of instability in time-independent inelastic solids, Arch. Mech., Volume 43 (1991), pp. 519-545

[4] B. Fedelich; A. Ehrlaher An analysis of stability of equilibrium and of quasi-static transformations on the basis of the dissipation function, Eur. J. Mech. A Solids, Volume 16 (1997), pp. 833-855

[5] M. Ortiz; E.A. Repetto Nonconvex energy minimization and dislocation structures in ductile single crystals, J. Mech. Phys. Solids, Volume 36 (1999), pp. 286-351

[6] C. Miehe; J. Schotte; M. Lambrecht Homogenization of inelastic solid materials at finite strains based on incremental minimization principles. Application to the texture analysis of polycrystals, J. Mech. Phys. Solids, Volume 50 (2002), pp. 2123-2167

[7] R. Hill Some basic principles in the mechanics of solids without a natural time, J. Mech. Phys. Solids, Volume 7 (1959), pp. 209-225

[8] R. Hill Aspects of invariance in solids mechanics, Adv. Appl. Mech., 18, Academic Press, New York, 1978, pp. 1-75

[9] H. Petryk; K. Thermann On discretized plasticity problems with bifurcations, Int. J. Solids Structures, Volume 29 (1992), pp. 745-765

[10] H. Petryk; K. Thermann Post-critical plastic deformation in incrementally nonlinear materials, J. Mech. Phys. Solids, Volume 50 (2002), pp. 925-954

[11] H. Petryk Stability and constitutive inequalities in plasticity (W. Muschik, ed.), CISM Courses and Lectures, Vol. 336, Springer, Wien, 1993, pp. 259-329

[12] H. Petryk Second-order work and dissipation on indirect paths, C. R. Mecanique, Volume 330 (2002), pp. 121-126

[13] Q.S. Nguyen Stability and Nonlinear Solid Mechanics, Wiley, Chichester, 2000

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